Shuping Shi

Testing for Multiple Bubbles: Historical Episodes of Exuberance and Collapse in the S&P 500

Recent work on econometric detection mechanisms has shown the effectiveness of recursive procedures in identifying and dating financial bubbles. These procedures are useful as warning alerts in surveillance strategies conducted by central banks and fiscal regulators with real time data. Use of these methods over long historical periods presents a more serious econometric challenge due to the complexity of the nonlinear structure and break mechanisms that are inherent in multiple bubble phenomena within the same sample period. To meet this challenge the present paper develops a new recursive flexible window method that is better suited for practical implementation with long historical time series. The method is a generalized version of the sup ADF test of Phillips, Wu and Yu (2011, PWY) and delivers a consistent date-stamping strategy for the origination and termination of multiple bubbles. Simulations show that the test significantly improves discriminatory power and leads to distinct power gains when multiple bubbles occur. An empirical application of the methodology is conducted on S&P 500 stock market data over a long historical period from January 1871 to December 2010. The new approach successfully identifies the well-known historical episodes of exuberance and collapse over this period, whereas the strategy of PWY and a related CUSUM dating procedure locate far fewer episodes in the same sample range.

Testing for Multiple Bubbles

Identifying and dating explosive bubbles when there is periodically collapsing behavior over time has been a major concern in the economics literature and is of great importance for practitioners. The complexity of the nonlinear structure inherent in multiple bubble phenomena within the same sample period makes econometric analysis particularly difficult. The present paper develops new recursive procedures for practical implementation and surveillance strategies that may be employed by central banks and fiscal regulators. We show how the testing procedure and dating algorithm of Phillips, Wu and Yu (2011, PWY) are affected by multiple bubbles and may fail to be consistent. The present paper proposes a generalized version of the sup ADF test of PWY to address this difficulty, derives its asymptotic distribution, introduces a new date-stamping strategy for the origination and termination of multiple bubbles, and proves consistency of this dating procedure. Simulations show that the test significantly improves discriminatory power and leads to distinct power gains when multiple bubbles occur. Empirical applications are conducted to S&P 500 stock market data over a long historical period from January 1871 to December 2010. The new approach identifies many key historical episodes of exuberance and collapse over this period, whereas the strategy of PWY and the CUSUM procedure locate far fewer episodes in the same sample range.

Testing for Multiple Bubbles: Limit Theory of Real Time Detectors

This article provides the limit theory of real‐time dating algorithms for bubble detection that were suggested in Phillips, Wu, and Yu (PWY; International Economic Review 52 [2011], 201–26) and in a companion paper by the present authors (Phillips, Shi, and Yu, 2015; PSY; International Economic Review 56 [2015a], 1099–1134. Bubbles are modeled using mildly explosive bubble episodes that are embedded within longer periods where the data evolve as a stochastic trend, thereby capturing normal market behavior as well as exuberance and collapse. Both the PWY and PSY estimates rely on recursive right‐tailed unit root tests (each with a different recursive algorithm) that may be used in real time to locate the origination and collapse dates of bubbles. Under certain explicit conditions, the moving window detector of PSY is shown to be a consistent dating algorithm even in the presence of multiple bubbles. The other algorithms are consistent detectors for bubbles early in the sample and, under stronger conditions, for subsequent bubbles in some cases. These asymptotic results and accompanying simulations guide the practical implementation of the procedures. They indicate that the PSY moving window detector is more reliable than the PWY strategy, sequential application of the PWY procedure, and the CUSUM procedure.

Specification Sensitivity in Right‐Tailed Unit Root Testing for Explosive Behaviour

This article aims to provide some empirical guidelines for the practical implementation of right-tailed unit root tests, focusing on the recursive right-tailed ADF test of Phillips et al. (2011b). We analyze and compare the limit theory of the recursive test under different hypotheses and model specifications. The size and power properties of the test under various scenarios are examined and some recommendations for empirical practice are given. Some new results on the consistent estimation of localizing drift exponents are obtained, which are useful in assessing model specification. Empirical applications to stock markets illustrate these specification issues and reveal their practical importance in testing.

Dating the timeline of house price bubbles in Australian capital cities

House prices in some Australian capital cities have recently been on the rise to the extent that some describe this as an emerging bubble, but this claim remains formally untested to date. We apply a recently developed time series procedure to detect, and time‐stamp, bubbles in house price to rent ratios in Australian capital cities. The results show a sustained, yet varying, degree of speculative behaviour in all capital cities in the 2000s before the 2008 global financial crisis (GFC) engulfing different housing markets. The onset of these bubbles was soon after the federal government introduced a major change to the capital gains tax law, and all of these bubbles collapsed with or before the GFC. As of January 2016 only Sydney exhibits significant evidence of an exuberant rise in house prices compared to rents. We believe that the method we apply has the potential to be a general early warning indicator to detect housing bubbles in other countries/markets. We provide the programming files to enable researchers to implement this test in other countries.

Financial bubble implosion and reverse regression

Expansion and collapse are two key features of a financial asset bubble. Bubble expansion may be modeled using a mildly explosive process. Bubble implosion may take several different forms depending on the nature of the collapse and therefore requires some flexibility in modeling. This paper first strengthens the theoretical foundation of the real time bubble monitoring strategy proposed in Phillips, Shi and Yu (2015a,b, PSY) by developing analytics and studying the performance characteristics of the testing algorithm under alternative forms of bubble implosion which capture various return paths to market normalcy. Second, we propose a new reverse sample use of the PSY procedure for detecting crises and estimating the date of market recovery. Consistency of the dating estimators is established and the limit theory addresses new complications arising from the alternative forms of bubble implosion and the endogeneity effects present in the reverse regression. A real-time version of the strategy is provided that is suited for practical implementation. Simulations explore the finite sample performance of the strategy for dating market recovery. The use of the PSY strategy for bubble monitoring and the new procedure for crisis detection are illustrated with an application to the Nasdaq stock market.

Did bubbles migrate from the stock to the housing market in China between 2005 and 2010

The speculative nature of both stock and housing markets in China has attracted the attention of observers. However, while stock market data are easily available, the low frequency and low quality of publicly available housing price data hampers the study of the relationship between the two markets. We use original hedonic weekly resale housing prices of a major Chinese housing market and study them in conjunction with Shanghais stock market index in the second half of the 2000s. The use of the Phillips et al. (2015 a,b) recursive explosive-root test enables us to detect and date speculative episodes in both markets. We then implement the Greenaway-McGrevy and Phillips (2016) methodology to detect the presence of migration between the two types of bubbles. We detect significant migration from the stock to the housing market bubble in 2009 and a temporary spillover in 2007.

Financial Bubble Implosion

Expansion and collapse are two key features of a financial asset bubble. Bubble expansion may be modeled using a mildly explosive process. Bubble implosion may take several different forms depending on the nature of the collapse and therefore requires some flexibility in modeling. This paper develops analytics and studies the performance characteristics of the real time bubble monitoring strategy proposed in Phillips, Shi and Yu (2014b,c, PSY) under alternative forms of bubble implosion that can be represented in terms of mildly integrated processes which capture various return paths to market normalcy. We propose a new reverse sample use of the PSY procedure for detecting crises and estimating the date of market recovery. Consistency of the dating estimators is established and the limit theory addresses new complications arising from the alternative forms of bubble implosion and the endogeneity effects present in the reverse regression. Simulations explore the finite sample performance of the strategy for dating market recovery and an illustration to the Nasdaq stock market is provided. A real-time version of the strategy is provided that is suited for practical implementation.

Energy Consumption and Economic Growth in the United States

We study the relationship between energy consumption and real GDP in the United States using a multivariate time-varying model [1973Q1-2014Q1]. We show that the combination of disaggregation into specific fuels and time variation gives more nuanced results than the alternatives for the U.S. Specifically, we find that the Granger causal relationship between total energy and real U.S. GDP is bi-directional through much of the 1990s (the feedback hypothesis) but uni-directional running from real U.S. GDP to energy consumption in the 2000s (the conservation hypothesis). Similar pattern of changes was observed in the causal relationship between coal consumption and real U.S. GDP. Oil consumption largely supports the feedback hypothesis, especially after 2009. Natural gas consumption shows a brief period supporting the conservation hypothesis in the early-to-mid 2000s, but primarily supports the neutrality hypothesis that natural gas consumption and economic growth are independent.

Bubble Detection and Sector Trading in Real Time

We conduct a pseudo real-time analysis of the existence and extent of speculative bubbles in 11+ US sectors over the period January 1973–May 2015. Based on computed bubble signals, a trading strategy is constructed which switches funds between the market index and those industry sectors that exhibit bubble dynamics. Our strategy generates the highest after-transaction-cost return and Sharpe ratio, and first-order stochastically dominates a range of alternative strategies we consider, including the buy-and-hold investment in the market index. Subsample analysis and specification checks confirm the robustness of our findings.